Bifurcation in growth patterns for arrays of parallel Griffith, edge and sliding cracks

This paper presents the recent finding by Muhlhaus et al [1] that bifurcation of crack growth patterns exists for arrays of two-dimensional cracks. This bifurcation is a result of the nonlinear effect due to crack interaction, which is, in the present analysis, approximated by the dipole asymptotic or pseudo-traction method. The nonlinear parameter for the problem is the crack length/ spacing ratio lambda = a/h. For parallel and edge crack arrays under far field tension, uniform crack growth patterns (all cracks having same size) yield to nonuniform crack growth patterns (i.e. bifurcation) if lambda is larger than a critical value lambda(cr) (note that such bifurcation is not found for collinear crack arrays). For parallel and edge crack arrays respectively, the value of lambda(cr) decreases monotonically from (2/9)(1/2) and (2/15.096)(1/2) for arrays of 2 cracks, to (2/3)(1/2)/pi and (2/5.032)(1/2)/pi for infinite arrays of cracks. The critical parameter lambda(cr) is calculated numerically for arrays of up to 100 cracks, whilst discrete Fourier transform is used to obtain the exact solution of lambda(cr) for infinite crack arrays. For geomaterials, bifurcation can also occurs when array of sliding cracks are under compression.

Tillage and traffic effects on runoff

Traffic and tillage effects on runoff and crop performance on a heavy clay soil were investigated over a period of 4 years. Tillage treatments and the cropping program were representative of broadacre grain production practice in northern Australia, and a split-plot design used to isolate traffic effects. Treatments subject to zero, minimum, and stubble mulch tillage each comprised pairs of 90-m 2 plots, from which runoff was recorded. A 3-m-wide controlled traffic system allowed one of each pair to be maintained as a non-wheeled plot, while the total surface area of the other received a single annual wheeling treatment from a working 100-kW tractor. Rainfall/runoff hydrographs demonstrate that wheeling produced a large and consistent increase in runoff, whereas tillage produced a smaller increase. Treatment effects were greater on dry soil, but were still maintained in large and intense rainfall events on wet soil. Mean annual runoff from wheeled plots was 63 mm (44%) greater than that from controlled traffic plots, whereas runoff from stubble mulch tillage plots was 38 mm (24%) greater than that from zero tillage plots. Traffic and tillage effects appeared to be cumulative, so the mean annual runoff from wheeled stubble mulch tilled plots, representing conventional cropping practice, was more than 100 mm greater than that from controlled traffic zero tilled plots, representing best practice. This increased infiltration was reflected in an increased yield of 16% compared with wheeled stubble mulch. Minimum tilled plots demonstrated a characteristic midway between that of zero and stubble mulch tillage. The results confirm that unnecessary energy dissipation in the soil during the traction process that normally accompanies tillage has a major negative effect on infiltration and crop productivity. Controlled traffic farming systems appear to be the only practicable solution to this problem.

Influence of imperfect interfaces on bending and vibration of laminated composite shells

This paper is devoted to modeling elastic behavior of laminated composite shells, with special emphasis on incorporating interfacial imperfection. The conditions of imposing traction continuity and displacement jump across each interface are used to model imperfect interfaces. Vanishing transverse shear stresses on two free surfaces of a shell eliminate the need for shear correction factors. A linear theory underlying elastostatics and kinetics of laminated composite shells in a general configuration is presented from Hamilton's principle. In the special case of vanishing interfacial parameters, this theory reduces to the conventional third-order zigzag theory for perfectly bonded laminated shells. Numerical results for bending and vibration problems of laminated circular cylindrical panels are tabulated and plotted to indicate the influence of the interfacial imperfection. (C) 2000 Elsevier Science Ltd. All rights reserved.